Tag Archives: linear algebra

How do I Create the Identity Matrix in R? Also a bit of group theory.

I googled for this once upon a time and nothing came up. Hopefully this saves someone ten minutes of digging about in the documentation. You make identity matrices with the keyword diag, and the number of dimensions in parentheses. > … Continue reading

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I feel vindicated in several ways by the Netflix Engineering team’s recent blog post explaining what they did with the results of the Netflix Prize. What they wrote confirms what I’ve been saying about recommendations as well as my experience … Continue reading

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Linear Transformations will take you on a Trip Comparable to that of Magical Mushroom Sauce, And Perhaps cause More Lasting Damage Long after I was supposed to “get it”, I finally came to understand matrices by looking at the above … Continue reading

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Angle = Volume

This is trippy, and profound. The determinant — which tells you the change in size after a matrix transformation 𝓜 — is just an Instance of the Alternating Multilinear Map. (Alternating meaning it goes + − + − + − + … Continue reading

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Positive Semi-Definite

Mathematical matrices are blocks of numbers. So they don’t necessarily have definite characteristics the way plain vanilla, singleton numbers do. They’re freer. For example 131 ∈ positive and −9 ∈ negative. But is positive, negative, or zero? Well, it has … Continue reading

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Jacobian

In the world of linear approximations of multiple parameters and multiple outputs, the Jacobian is a matrix that tells you: if I twist this knob, how does that part of the output change? Pretend that a through z are parameters, or knobs … Continue reading

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Daubechies D20 Ingrid Daubechies constructed several orthogonal discrete wavelet bases. Wavelet bases span function space, which includes for example sound, video, and images. Orthogonal wavelets are independent of each other. Discrete wavelets are easy for computers to deal with.

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